Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 5 - Integration - 5.2 Definite Integrals - 5.2 Exercises: 3

Answer

Net area equals the area of the region if that region lies completely on, or above the $x$ axis. Net area differs from the area of the region if it partially lies below the $x$ axis.

Work Step by Step

When there are no pieces of some region lying below the $x$ axis then the net area of the region is just the sum of the areas of the pieces which is exactly equal to its area. When there are pieces of some region below the $x$ axis then when we calculate the net area of such a region we subtract the areas of those pieces and get a value that is different than the area of the region.
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